PRP Records

Probable Primes Top 10000

(224926 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
80012^204323-222161508Yves Minet08/2013
80032^204317-19561506Lelio R Paula08/2011
80023^128910-8661506Lelio R Paula04/2013
80042^204318+7453961506Enzo Doria04/2016
8005(2^204334-3)/114133361505Lelio R Paula03/2012
80062^204297-103609361500Paul Bourdelais11/2012
80073^128880+5861492Lelio R Paula04/2013
80082^204216-11167761476Enzo Doria05/2014
8009(F(73524)^5-F(73523)^5)/F(73522)61462Wayne Halsdorf03/2012
80102^204129+20412961449Henri Lifchitz04/2002
80113^128787+2^(128787-1)61448Robert Price05/2016
801211^58999-7861442Lelio R Paula05/2013
80132^204083-11196761436Enzo Doria05/2014
8014(45^37159+1)/4661431Robert Price11/2013
8015677^21702+21702^67761430Norbert Schneider06/2016
801614837^13810+13810^1483761429Hans Havermann02/2017
8017(7*2^204043+1)/3961423Lelio R Paula03/2012
801811^58976-174061418Enzo Doria11/2012
80192^204016-1608561415Enzo Doria04/2013
8020V(379967)61393Serge Batalov03/2015
802143777!3-3^4377761392Robert Price08/2015
80227^72642+8861390Lelio R Paula04/2013
80233^128656+3261385Lelio R Paula04/2013
80242^203916-1749361385Enzo Doria05/2013
80256^78880+2361381Lelio R Paula04/2013
8026(388*10^61374-1)/961376Robert Price11/2017
80272^203877-11179961374Enzo Doria05/2014
80282^203867-161561371Lelio R Paula10/2011
80294*10^61367+1961368Robert Price04/2016
8030(19*2^203854+1)/4231961363Lelio R Paula08/2012
8031L(293659)/7652812271961361Serge Batalov07/2017
80322^203825-1580561358Enzo Doria04/2013
80332^203816-1582561355Enzo Doria04/2013
80345*10^61348+5961349Robert Price09/2016
803521^46395-261345Lelio R Paula08/2013
8036(809*29^41946-165)/2861344Curtis Bright05/2015
80377*6^78826+561340Lelio R Paula09/2014
8038(3^128558+7)/8377316642969661324Lelio R Paula04/2012
80392^203706-11161322Lelio R Paula08/2011
804017567^3094+3094^1756761318Hans Havermann02/2017
80412^203689-3161317Thomas Masser10/2005
8042(11*2^203678-1)/5368961310Lelio R Paula01/2014
80432^203642+3961303Lelio R Paula08/2011
8044floor(Pi*10^61382)%(10^61303)61303Serge Batalov07/2012
804511^58849-604061285Enzo Doria02/2013
804643694!3-361264Robert Price10/2014
804758*(10^(3*20420)-1)/111-161260Robert Price10/2014
80482^203490+1290961257Lelio R Paula10/2011
8049(16*10^61251-31)/361252Robert Price03/2016
805020^47077-570361249Enzo Doria03/2013
80512^203434-11308161240Enzo Doria07/2014
80535^87606+461234Wojciech Florek11/2005
80522^203412-16761234Lelio R Paula08/2011
80542^203402+108961231Lelio R Paula10/2011
8055(8*10^61230+67)/361231Robert Price01/2017
8056(2^203408+lucasV(1,2,203408)+1)/(2*32993)61228Mike Oakes11/2016
80571265^19732+19732^126561211Serge Batalov05/2014
80582^203330+14561209Lelio R Paula08/2011
80596^78647-13761200Lelio R Paula04/2013
806085^31718+8461198Norbert Schneider10/2015
806111^58763-27061196Enzo Doria07/2012
80622^203285-11232161195Enzo Doria06/2014
80632^203253-99514361186Paul Bourdelais11/2012
806415319^9862+9862^1531961184Hans Havermann07/2016
80657^72395-4461181Lelio R Paula04/2013
8066(49*10^61167-67)/961168Robert Price08/2017
80675*2^203176-761163Lelio R Paula04/2014
8068(26*10^61156-413)/961157Robert Price10/2017
80707^72358+5461150Lelio R Paula04/2013
80692^203133-11177561150Enzo Doria05/2014
8071(lucasV(1,2,406356)+2)/(3^2*5*11*19*31*583697*9671743)61145Mike Oakes01/2017
80722^203112-1800961143Enzo Doria05/2013
807343607!3+72961129Robert Price09/2014
80742^203065-11485361129Enzo Doria05/2015
80753^128111+19661125Lelio R Paula04/2013
8076128^29007+29007^12861124Serge Batalov05/2014
80774*10^61119+4961120Robert Price08/2017
807822355*2^203009-361117Donovan Johnson03/2004
80792^203018+3361115Lelio R Paula08/2011
80802^203017-161561115Lelio R Paula10/2011
808116697^4570+4570^1669761110Hans Havermann12/2016
80822^202998-1724161109Enzo Doria05/2013
808320^46964+9361102Lelio R Paula06/2013
8084(55*10^61097-1)/961098Ray Chandler02/2012
808520^46960-546361097Enzo Doria03/2013
8086(11*10^61095+49)/361096Robert Price05/2016
80872^202934-595561090Lelio R Paula10/2011
808819^47772-6861089Lelio R Paula05/2013
80892^202877-49942361073Paul Bourdelais03/2013
80902^202763-1712561038Enzo Doria05/2013
8091(23*2^202756+1)/961037Lelio R Paula03/2012
809214788^13355+13355^1478861011Hans Havermann12/2016
809316069^6258+6258^1606961005Hans Havermann12/2016
80945^87276-1433661004Enzo Doria02/2013
809550^35899-49^3589960992Robert Price12/2012
80962^202599-304960989Yves Minet10/2014
80972^202535-11157160970Enzo Doria05/2014
8098(13*10^60966+107)/360967Robert Price11/2017
810010^60959+5760960Patrick De Geest12/2008
80996*10^60959-9160960Robert Price11/2017
810210^60959-6095960959Henri Lifchitz08/2002
810110^60959-2917760959Patrick De Geest08/2008
81035^87206+4^(87206+1)60955Robert Price07/2016
81042^202476-1590960952Enzo Doria04/2013
81052^202472-1751360951Enzo Doria05/2013
810614858^12651+12651^1485860950Hans Havermann12/2016
81072^202389-5869560926Lelio R Paula09/2011
81083^127597-3460880Lelio R Paula04/2013
810915088^10831+10831^1508860876Hans Havermann12/2016
81102^202198-11326160868Enzo Doria07/2014
81112^202182+13560863Lelio R Paula08/2011
81122^202176+8560862Lelio R Paula08/2011
81135183^16384+5182^1638460860Henri Lifchitz01/2007
8114(31*2^202163+1)/360859Lelio R Paula03/2012
811514708^13707+13707^1470860847Hans Havermann12/2016
81162^202112+202112^2-160842Robert Price04/2014
8117(13*2^202142-1)/40598427425760841Lelio R Paula01/2014
811864743*10^60832+(6^78175-11)/560837Gilbert Mozzo05/2012
8119(19*2^202098-1)/679560836Lelio R Paula01/2014
8120(6^78175-11)/560832Paul Bourdelais11/2011
81212^202063+160560828Lelio R Paula09/2011
81222^202058+85960826Lelio R Paula09/2011
81231576^19021+19021^157660821Serge Batalov05/2014
8124(2^202009+3)/600560807Lelio R Paula03/2012
812510^60776+360777Robert Price01/2011
812610^60776-1481960776Patrick De Geest12/2012
812755*10^60772+760774Robert Price10/2017
8128(6883*2^201869-1)/3560771Lelio R Paula04/2015
8129(27*2^201841-1)/4360760Lelio R Paula01/2014
81302^201822-17760755Lelio R Paula08/2011
8131(13*10^60744+17)/360745Robert Price06/2015
8132(31*2^201754-1)/9960734Lelio R Paula01/2014
8133(26*10^60717-71)/960718Robert Price03/2015
813437^38712-260709Lelio R Paula08/2013
81352^201657-11200360705Enzo Doria05/2014
8136(10^60703+3^60703)/1360702Robert Price01/2013
81372^201622-11281760695Enzo Doria06/2014
81382^201620-1717760694Enzo Doria05/2013
8139(2^201615-3)*6-760693Gilbert Mozzo05/2016
81402^201609-4978960691Henri Lifchitz03/2005
81412^201582-1906160683Enzo Doria05/2013
814243316!3+2760679Robert Price09/2014
8143(509203*2^201564-1)/506760679Lelio R Paula04/2015
81442^201560+10560676Lelio R Paula08/2011
8145(27*2^201584-1)/64675548645760673Lelio R Paula01/2014
81462^201545-1802160672Enzo Doria05/2013
81472^201543+1171560671Lelio R Paula09/2011
81482^201512-11175560662Enzo Doria05/2014
8149p(13013)#/2+6460662Robert Price03/2017
815011^58248+1660660Lelio R Paula05/2013
81512^201496-2760657Lelio R Paula08/2011
81525*10^60655+5760656Robert Price11/2017
8153(7*10^60643+197)/360644Robert Price07/2017
81542^201426-1609760636Enzo Doria04/2013
8155(17*10^60631-11)/360632Robert Price07/2015
81566^77916-7760631Lelio R Paula04/2013
8157(27*2^201410-1)/49160630Lelio R Paula01/2014
81585^86727+9860620Lelio R Paula04/2013
815917^49266-2660620Lelio R Paula05/2013
816020^46589-3360614Lelio R Paula05/2013
81616^77889+6560610Lelio R Paula04/2013
8162139901#+14838760595Nicolas PALAU09/2016
81632^201285-11172360593Enzo Doria05/2014
816446199*2^201268+12964760593Paul Vanderveen11/2016
81663^126991-10060591Lelio R Paula04/2013
81652^201278-11162360591Enzo Doria05/2014
81675^86682-1600460589Enzo Doria05/2014
8168(865*10^60583-1)/960585Robert Price11/2017
8169(58*10^60579+221)/960580Robert Price02/2017
81709*2^201231-560578Lelio R Paula04/2014
81714*10^60572-8960573Robert Price08/2017
8172(78557*2^201207+1)/1306760571Lelio R Paula06/2014
81732^201186-6694560564Lelio R Paula09/2011
81742^201186-9439560564Lelio R Paula09/2011
817565^33403+3260557Lelio R Paula01/2016
8176103^30079+10260545Norbert Schneider10/2016
8177(1000159^10091+1)/100016060541Faysal YAtim08/2008
81782^201098-1771760537Enzo Doria05/2013
8179(3^126881+8)/482960534Lelio R Paula03/2012
81802^201074+7504960530Enzo Doria04/2016
818111^58111-129060517Enzo Doria11/2012
8182(509203*2^201012-1)/960516Lelio R Paula04/2015
81832^200911+571160481Lelio R Paula10/2011
8184(2^200912-3)/2360480Lelio R Paula03/2012
818518^48179-17^4817960478Jean-Louis Charton12/2010
818738^38281-37^3828160476Robert Price09/2012
81864*7^71560-360476Lelio R Paula09/2014
8188(10^(2*30232+1)+15*10^30232-1)/360465Robert Price04/2016
8189lucasV(1,2,401712)+260464Mike Oakes01/2017
81902^200833-1849360457Enzo Doria05/2013
819120^46465-504360453Enzo Doria03/2013
81922^200810-1825760450Enzo Doria05/2013
8193((2)^(2*100400-1)+(2)^(100400-1)+1)+2667260447Faysal YAtim04/2018
81945^86466-1433660438Enzo Doria02/2013
8195Phi(145558,10)/103928413/161714939/14779231531/36075385837/24241141985360432Maksym Voznyy10/2011
8196(29*2^200703-1)/23160417Lelio R Paula01/2014
81972^200682-101683160412Paul Bourdelais11/2012
81982^200617-1788160392Enzo Doria05/2013
8199(25^43201+1)/2660391Robert Price06/2013
82012^200609-13360390Lelio R Paula08/2011
82002^200608-1283760390Enzo Doria10/2012
82022^200607-1712160389Enzo Doria05/2013
820311^57975-162060375Enzo Doria11/2012
8204(9913*2^200538-1)/380160369Lelio R Paula04/2015
82055^86342+6460351Lelio R Paula04/2013
8206(14*10^60346-23)/960347Robert Price04/2015
82072^200457-829560344Lelio R Paula09/2011
82086^77546+11360343Lelio R Paula04/2013
821037^38461-36^3846160315Robert Price06/2012
82092^200361-1759360315Enzo Doria05/2013
821110103^15059-10660304Enzo Doria07/2012
82122^200301-1740160297Enzo Doria05/2013
8213(37*10^60290+71)/960291Robert Price04/2015
82142^200266-9439560287Lelio R Paula09/2011
82152^200261-11161360285Enzo Doria05/2014
821646^36238-4560256Norbert Schneider07/2014
821713^54091+9460255Lelio R Paula05/2013
8218311^24171-15460253Enzo Doria07/2012
82192^200120-8108960243Paul Bourdelais01/2012
82203^126262+868060243Lelio R Paula04/2013
822143031!3-5904960239Robert Price12/2015
82222^200100-11126960237Enzo Doria05/2014
8223(29*2^200069-1)/537360225Lelio R Paula01/2014
822420^46283-192360216Enzo Doria03/2013
82252^200011-11207560210Enzo Doria05/2014
82262^200002+7453960207Enzo Doria04/2016
8227(38602791*2^200026-1)/(577849*2645749*3427009)60203Jens K. Andersen09/2007
8228(28*10^60180+149)/360181Robert Price10/2017
82292^199872+9360168Donovan Johnson06/2008
82306^77321+7760168Lelio R Paula04/2013
8231(86*10^60165-77)/960166Robert Price05/2016
8232(2^199868+78557)/2337360162Lelio R Paula05/2012
82337^71180+8260155Lelio R Paula04/2013
82352^199814-11229560151Enzo Doria06/2014
8234(51^35227-1)/5060151Paul Bourdelais08/2017
823642964!3-8160135Robert Price09/2014
82372^199709-5160119Lelio R Paula05/2011
82382^199700-11162360116Enzo Doria05/2014
8239(15185*2^199681-1)/15960112Lelio R Paula04/2015
82402^199672+253360108Henri Lifchitz09/2004
824120^46198-1160105Lelio R Paula04/2013
82422^199657+9325760103Yves Minet03/2010
82433^125967-11060102Lelio R Paula10/2012
82442^199654-1881360102Enzo Doria05/2013
8245(29*10^60100+19)/360101Robert Price01/2017
82462^199615-2*199615+160091Robert Price04/2018
8247129^28468+28468^12960085Serge Batalov05/2014
82482^199572-1587360078Enzo Doria04/2013
82499*2^199559+760075Lelio R Paula03/2014
82502^199527-11191960064Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 18 2018 22:22 (Time in France)

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